The technique of modulation on multiple carriers, referred to as OFDM, is known and consists of distributing the data to be transmitted over a large number of sub-carriers, which makes it possible to obtain a symbol time appreciably longer than the spread of the pulse response of the transmission channel between a transmitter and a receiver of the said transmission system. This technique is perfectly adapted to radio transmissions, with fixed, mobile or portable reception.
A description of a transmission system of the OFDM (Orthogonal Frequency Division Multiplex) type can be found in an article entitled “Principles of modulation and channel coding for digital broadcasting for mobile receivers”, which appeared in EBU Review no 224, pp 168-190 of August 1987 in the name of R. Lasalle and M. Alard.
Such a transmission system is depicted in FIG. 1 and is now described. It consists essentially of a transmitter 10 in communication with a receiver 20 by means of a transmission channel 30.
The data to be transmitted are first of all subject, in a unit 12, to a binary to signal coding which consists of a process of modulation, for example, a modulation of the QPSK (Quadrature Phase Shift Keying) type, or of the 16 QAM (16 Quadrature Amplitude Modulation) type, or of the 64 QAM type. The unit 12 delivers signals which are hereinafter referred to as modulation signals and which belong to a modulation alphabet which depends on the type of modulation used by the unit 12.
In a framing unit 13, the modulation signals delivered by the unit 12 are then put in the form of frames with possibly the insertion of reference signals (insertion of reference symbols, insertion of distributed pilots, etc) which may prove necessary to certain processings, on the receiver side, such as synchronization processings.
The modulation signal frames delivered by the unit 13 modulate, in a unit 14, a plurality of sub-carriers with distinct Respective frequencies. This modulation carried out by the unit 14 consists, for example, of the application of an inverse Fourier transform to blocks of modulation signals contained in the frames issuing from the unit 13. The unit 14 delivers signals which are hereinafter referred to as OFDM symbols.
The OFDM symbols issuing from the modulation unit 14 are subject to a digital to analogue conversion in a conversion unit 15.
All the processings implemented in the transmitter 10 are synchronized by means of a time base so that the OFDM symbols delivered by the modulation unit 14 are delivered at a sampling frequency feE referred to as the transmitter sampling frequency.
It should be noted that the modulation unit 14 can provide a guard time between each OFDM symbol, which makes it possible to reduce, or even eliminate, any interference between consecutive symbols. For example, the guard time of a symbol is a replica of the end of the previous symbol and its length is chosen so that its duration is greater than that of almost all the echoes to which the transmission channel 30 is subject.
It should be noted that the data to be transmitted can previously be subject to a coding which can be of the type with convolution, of the type with convolution with an external Reed-Solomon code, of the type with codes referred to as turbo-codes or others. They can also have been subject to an interleaving which can be of the frequency type, that is to say an interleaving of the length of an OFDM symbol, or of the frequency and time type, notably when the interleaving extends over a larger number of symbols. This term “frequency and time interleaving” refers to the time-frequency representation of the OFDM signal.
FIG. 2 depicts an OFDM symbol with a guard time GI of duration TGI and a part containing the useful data of duration TU. The total duration of the symbol is denoted TS.
The analogue signal delivered by the unit 15 is then transmitted by a transmission unit 17 over the transmission channel 30 modulating a carrier at a frequency, denoted in the remainder of the description f0E The frequency f0E is also generated by the time base 16.
It should also be noted that the transmitter sampling frequency feE could be proportional to the transmission carrier frequency f0E.
In order to recover the transmitted data, the receiver 20 performs the operations which are the inverse of those performed by the transmitter 10. To do this, the receiver 20 has a receiving unit 27 designed to transpose into baseband the signal received from the channel 30 by means of a carrier detection signal of frequency f0R delivered by the time base 26. The sampling frequency feR is possibly proportional to the carrier detection frequency f0R.
The receiver 20 also comprises an analogue to digital conversion unit 21 which is provided for delivering digital samples to the input of a unit 22 providing the demodulation of the sub-carriers which were used during the modulation performed by the modulation unit 14 of the transmitter 10.
According to one possible embodiment, the demodulation unit 22 uses a Fourier transform.
From the signal delivered by the demodulation unit 22, an estimation unit 23 performs an estimation of the modulation signals which were transmitted by the unit 12. To do this, the estimation unit 23 performs a correction of the phase shift and the amplitude changes caused by the multipath transmission channel 30.
The demodulated symbols are then decoded in a decoding unit 24 which is the dual of the coding unit 12:
All the units 21 to 24 are synchronized and, to do this, are clocked, by means of a time base 26, at a frequency which is related to a sampling frequency feR, referred to in the remainder of the description as the receiver sampling frequency. In particular, the signal delivered by the conversion unit 21 is in the form of samples clocked at this receiver sampling frequency feR. As for the unit 22, this demodulates blocks of samples which are grouped together within a window, hereinafter referred to as the analysis window, determined from a clock signal at a frequency related to the said receiver sampling frequency feR.
FIG. 2 depicts this analysis window F positioned at a time tn with respect to the start of the symbol under consideration.
It should be noted that, if the demodulation unit 22 ignores the data outside the analysis window, it does not carry but analysis of the samples constituting the guard time.
The estimation unit 23 can have a deframing unit 23a and a demodulation unit proper 23b. The demodulation unit 23b performs a demodulation which can be either a coherent demodulation with or without reference symbols, with or without pilots, or a differential demodulation according to the modulation performed by the coding unit 13. In the case of a coherent demodulation, an estimation of the frequency response of the channel 30 is performed in a unit 23c. 
The receiver 20 of such a telecommunications system, like any telecommunications system, poses the problem of its time synchronization and, in particular, the slaving of the receiver sampling frequency feR to the transmitter sampling frequency feE.
When this slaving is perfectly achieved, that is to say when the receiver sampling frequency feR is equal to the transmitter sampling frequency feE the processings performed in the receiver 20 are perfectly synchronized with the signal received from the transmitter 10. In particular, the position of the analysis window F used by the demodulation unit 22 can be determined so as to correspond exactly with the symbol to be demodulated.
In addition, as a result in particular of the use of a guard time, there is a certain tolerance on the position of this window.
However, the shift of the receiver sampling frequency feR with respect to the transmitter sampling frequency feE has three main consequences on the demodulation process:                a loss of orthogonality between the base functions of the received signal and the base functions used for demodulation, resulting in interference between the signals modulating the different sub-carriers of the same OFDM symbol (the distortion introduced then is generally very low and can be considered to be negligible, which is done by the invention),        a slipping of the analysis window which results in interference between consecutive OFDM symbols when this slippage is greater than an acceptable range, and        a phase shift between the demodulated signals of two consecutive symbols, a phase shift varying from carrier to carrier and directly related to the variation in the position of the analysis window.        
Conventionally, in order to solve this problem of slaving, a feedback loop is used which slaves the receiver sampling frequency feR to the transmitter sampling frequency feE, using the analysis of the signals received from the transmitter. However, this solution proves to be relatively cumbersome to implement as a result in particular of the use of a voltage controlled crystal oscillator (VCXO) which is also expensive.